Tue, 18 Oct 2011

16:00 - 17:00
L1

LMS Aitken Lecture: "Matroid Representation over Infinite Fields"

Professor Geoff Whittle
(Victoria University of Wellington)
Abstract

 

A canonical way to obtain a matroid is from a finite set of vectors in a vector space over a field F. A matroid that can be obtained in such a way is said to be representable over F. It is clear that when Whitney first defined matroids he had matroids representable over the reals as his standard model, but for a variety of reasons most attention has focussed on matroids representable over finite fields.
There is increasing evidence that the class of matroids representable over a fixed finite field is well behaved with strong general theorems holding. Essentially none of these theorems hold if F is infnite. Indeed matroids representable over the real-- the natural matroids for our geometric intuition -- turn out to be a mysterious class indeed. In the talk I will discuss this striking contrast in behaviour.

 

Wed, 16 Nov 2011
17:00
L1

Theory of Wind-Driven Sea

Professor Vladimir Zakharov
(Department of Mathematics)
Abstract

The self-consistent analytic theory of the wind-driven sea can be developed due to the presence of small parameter, ratio of atmospheric and water densities. Because of low value of this parameter the sea is "weakly nonlinear" and the average steepness of sea surface is also relatively small. Nevertheless, the weakly nonlinear four-wave resonant interaction is the dominating process in the energy balance. The wind-driven sea can be described statistically in terms of the Hasselmann kinetic equation.

This equation has a rich family of Kolmogorov-type solutions perfectly describing "rear faces" of wave spectra right behind the spectral peak.

More short waves are described by steeper Phillips spectrum formed by ensemble of microbreakings. From the practical view-point the most important question is the spatial and temporal evolution of spectral peaks governed by self-similar solutions of the Hasselmann equation. This analytic theory is supported by numerous experimental data and computer

simulations.   

Tue, 21 Jun 2011

14:00 - 15:00
L1

An introduction to integer factorization

Jan Tuitman
(Oxford)
Abstract

(Note change in time and location)

The purpose of this talk is to give an introduction to the theory and

practice of integer factorization. More precisely, I plan to talk about the

p-1 method, the elliptic curve method, the quadratic sieve, and if time

permits the number field sieve.

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